What might be the most likely cause for a horse to run in during the mile---?? No hike ---no nod....
First off, I am assuming you mean the horse is staying on gait, but is bearing in.
If I would ever post or say "Run in" ,I would mean the horse is on the literal run.
Second, Is the horse bearing in all the time? If so get out your copy of Care and Training and start reading.
My experience has been that most all horses will bear in on the turns and out on the stretches.
Why in on the turns. Horses are no dummies. They know the shortest way around.
Why out in the stretches. Their own centrifugal force will care them out as they come out of a turn.
If you think a horse may be bearing in on the turns because of lameness or a bad gait, then train him going the opposite way of the track, and see if he still wants to go to the left.
Good luck and good reading.
These types of problems have turned many a good horse trainer into a down and out drunk.